GMAT math formulas: the cheat sheet you actually need.
Every formula tested on GMAT Focus Quant, organized by topic with a one-line when-to-use note for each. No calculator and no formula sheet on test day — so the high-frequency ones have to live in your head.
The GMAT hands you nothing. On the Quantitative section there is no on-screen calculator and there is no formula sheet, on any section, ever. Whatever you need to compute, you compute by hand, and whatever formula you need, you supply from memory. That changes what a cheat sheet is for. This is not a document to glance at during the exam — you can't. It is a drilling tool. Read it, cover a column, recite the other, and keep doing that until recall is automatic. The goal is to make the formula appear in your head the instant you recognize the question type.
A formula you can look up is useless on test day, because you can't look anything up. The only formulas that count are the ones you can produce cold, under the clock, with no prompt.
Quant on the Focus Edition is Problem Solving only: 21 questions in 45 minutes, multiple choice. Data Sufficiency now lives in Data Insights. The formulas below cover the full Quant content map. Each table pairs the formula with a one-line note on when to reach for it, because knowing a formula and knowing when it applies are two different skills, and the GMAT tests the second one harder.
Arithmetic
The unglamorous foundation. Percent and ratio questions are everywhere on Quant and bleed into the word problems, so fluency here pays off across the whole section.
| Formula | Use it when… |
|---|---|
| Percent change = (new − old) / old × 100 | a value goes up or down and you need the percentage, not the raw difference. Always divide by the original value. |
| Increase by p% → multiply by (1 + p/100); decrease → multiply by (1 − p/100) | chaining successive changes. A 20% rise then a 20% fall is ×1.2×0.8 = 0.96, not back to start. |
| x% of y = (x/100) × y = y% of x | translating “percent of” into arithmetic; the swap trick makes some calculations far easier. |
| Fraction ↔ decimal ↔ percent equivalents | you want to skip long division. Know 1/8 = 0.125 = 12.5%, 1/6 ≈ 16.7%, 1/3 ≈ 33.3%, and the rest of the common set on sight. |
| Ratio a : b means parts; total = a + b parts | a quantity is split in a given ratio. Scale every part by the same multiplier to recover actual amounts. |
Number properties
High-frequency and almost never requiring heavy computation — these reward structure over arithmetic. Prime factorization is the master key to most of them.
| Rule / formula | Use it when… |
|---|---|
| Divisibility: by 3 if digit sum divisible by 3; by 9 if digit sum by 9; by 4 if last two digits by 4; by 6 if even and divisible by 3 | testing factors fast without dividing. Combine the rules for composite divisors. |
| GCF & LCM via prime factorization (GCF = lowest powers shared; LCM = highest powers present) | you need the largest common factor or smallest common multiple. Also: GCF × LCM = product of the two numbers. |
| Units-digit cycles (e.g. powers of 2 cycle 2, 4, 8, 6) | a question asks for the last digit of a large power. Find the cycle length, then take the exponent mod that length. |
| Remainder form: n = dk + r, with 0 ≤ r < d | reasoning about remainders. The remainder r is what matters; d is the divisor and k is the quotient. |
Algebra
Less about exotic formulas and more about recognizing patterns instantly. The factoring identities below show up constantly, often disguised, and spotting them turns a grind into one line.
| Formula | Use it when… |
|---|---|
| Linear: solve ax + b = c → x = (c − b)/a | one unknown, one equation. For two unknowns, use substitution or elimination across two equations. |
| Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a | a quadratic won't factor cleanly. The discriminant b² − 4ac tells you how many real roots exist. |
| Difference of squares: a² − b² = (a + b)(a − b) | you see two squares subtracted. One of the highest-value patterns on the test; it collapses ugly expressions fast. |
| Perfect squares: (a ± b)² = a² ± 2ab + b² | expanding a binomial square, or recognizing one to factor in reverse. Watch the middle 2ab term. |
| FOIL: (a + b)(c + d) = ac + ad + bc + bd | multiplying any two binomials by hand. First, Outer, Inner, Last — the systematic way to avoid dropping a term. |
Exponents and roots
Pure rules, no judgment calls — which makes them free points if memorized and silent score-killers if fuzzy. The negative and fractional cases trip people up the most.
| Rule | Use it when… |
|---|---|
| Product / quotient: xⁿ · xᵐ = xⁿ⁺ᵐ; xⁿ / xᵐ = xⁿ⁻ᵐ | same base, multiplied or divided. Add or subtract the exponents; never multiply the bases. |
| Power of a power: (xⁿ)ᵐ = xⁿᵐ | an exponent is raised to another exponent. Multiply them. |
| Negative exponent: x⁻ⁿ = 1 / xⁿ | you want to clear a negative power. Flip the base to the denominator and make the exponent positive. |
| Fractional exponent: xᵐ⁄ⁿ = ⁿ√(xᵐ) | a root is written as a power, or vice versa. The denominator is the root, the numerator is the power. |
| Root rules: √(ab) = √a · √b; √(a/b) = √a / √b | simplifying radicals. Pull perfect-square factors out from under the root. |
Word problems
The translation tax. The arithmetic is rarely hard; converting a sentence into the right equation is where points are won and lost. These four templates cover the overwhelming majority of Quant word problems.
| Formula | Use it when… |
|---|---|
| Distance = rate × time (D = RT) | anything moves. Build a small table of distance, rate, and time for each traveler, then relate them. |
| Combined work rate: 1/a + 1/b = 1/t (rates add) | two or more agents work together. Add their per-unit rates, not their times, to get the shared rate. |
| Weighted average = Σ(value × weight) / Σ weights | mixing groups of different sizes, or blending solutions of different concentrations. The bigger group pulls the average toward it. |
| Simple interest: I = Prt. Compound: A = P(1 + r/n)ⁿᵑ | a question specifies simple vs. compound. Simple grows on principal only; compound grows on principal plus prior interest. |
Statistics
The GMAT loves descriptive stats because they reward understanding over calculation. You will almost never compute a standard deviation by hand — but you must know what it measures and how a data shift affects it.
| Formula / concept | Use it when… |
|---|---|
| Mean = sum of values / count | the question says “average.” Often you're given the mean and count and must back out the sum. |
| Median = middle value (or average of the two middle) | data is skewed or has outliers. Order the set first; the median ignores how extreme the tails are. |
| Range = greatest − least | you need a quick measure of total spread. It only sees the two endpoints. |
| Standard deviation = spread around the mean (conceptual) | comparing how tightly clustered two sets are. Adding a constant to every value leaves SD unchanged; multiplying scales it. |
| Evenly spaced set: sum = average × count; average = (first + last)/2 | summing a consecutive or arithmetic sequence. Pairing the ends gives the average instantly. |
| Count = (last − first)/step + 1 | counting terms in an evenly spaced list. The “+ 1” is the classic off-by-one trap. |
Counting and probability
The smallest topic by volume but the one students fear most. The whole area reduces to a few ideas: multiply independent choices, decide whether order matters, and count the complement when direct counting is messy.
| Formula | Use it when… |
|---|---|
| Fundamental counting principle: total = n₁ × n₂ × … | independent stages each have their own number of choices. Multiply across the stages. |
| Permutations: nPr = n! / (n − r)! | order matters — arrangements, rankings, seatings. ABC and CBA count as different outcomes. |
| Combinations: nCr = n! / [r!(n − r)!] | order does notmatter — choosing a group or committee. ABC and CBA are the same selection. |
| Probability = desired outcomes / total outcomes | outcomes are equally likely. Count the favorable cases and the total cases, then divide. |
| At least one: P(at least one) = 1 − P(none) | “at least one” appears and direct counting is ugly. Computing the complement is almost always faster. |
Geometry
The longest list, because geometry is formula-dense. The figures are usually not drawn to scale, so you reason from given values and these relationships, not from how the picture looks.
| Formula | Use it when… |
|---|---|
| Angles: triangle sums to 180°; straight line 180°; full circle 360° | any figure with unknown angles. Chase angles using these sums plus vertical and parallel-line rules. |
| Triangle area = ½ × base × height | you have a base and the perpendicular height. The height must be perpendicular to the chosen base, not a slanted side. |
| Pythagorean theorem: a² + b² = c² | a right triangle. Memorize the common triples 3-4-5 and 5-12-13 to skip the radical. |
| 45-45-90 sides in ratio 1 : 1 : √2 | an isosceles right triangle, or a square's diagonal. The hypotenuse is a leg times √2. |
| 30-60-90 sides in ratio 1 : √3 : 2 | a 30-60-90 triangle, or half of an equilateral. The side opposite 30° is the smallest. |
| Circle: circumference = 2πr; area = πr² | any circle problem. Diameter d = 2r; arcs and sectors are fractions of these by the central angle over 360°. |
| Slope = (y₂ − y₁)/(x₂ − x₁) | comparing line steepness or testing parallel (equal slopes) and perpendicular (negative reciprocals). |
| Distance = √[(x₂ − x₁)² + (y₂ − y₁)²] | finding the length of a segment in the coordinate plane. It's the Pythagorean theorem in disguise. |
| Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2) | you need the point halfway between two coordinates. Average the x-values and the y-values separately. |
| Box: volume = lwh; surface area = 2(lw + lh + wh) | a rectangular solid. Volume fills it; surface area wraps the six faces. |
| Cylinder: volume = πr²h; surface area = 2πr² + 2πrh | a cylinder. The lateral surface is the circumference times the height; add the two circular caps. |
What to actually memorize
You cannot brute-force this list by rote and expect it to hold under pressure. Split it in two. A small set of high-frequency formulas appears so often that hesitation costs you real time and points — those must be reflexive: percent change, D = RT, the combined work rate, the 30-60-90 and 45-45-90 special triangles, and nCr. Drill those until they fire without conscious effort.
Everything else, you derive from understanding rather than store as a fact. If you understand that area is base times height for a parallelogram, the triangle's half follows. If you understand FOIL, the perfect-square and difference-of-squares identities are just patterns you've seen enough times to recognize. The distance formula is the Pythagorean theorem with coordinates plugged in. Memorize the handful that need to be instant; build the rest on a foundation you can reconstruct when memory fails.
Memorize the high-frequency five cold. Derive the rest from understanding. A cheat sheet you can rebuild from principles is worth more than one you've only ever read.
The platform
Zakarian GMAT's Quant chapters teach each of these formulas in context, then immediately put them to work in graded problem sets so the recall is built through retrieval rather than re-reading. The error log's tags surface whether a miss was a formula gap or a misapplication, which tells you exactly which row of this cheat sheet to drill next. The sample chapter is free if you want to see the teaching first.
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